Intermolecular vibrations and fast relaxations in supercooled ionic liquids

Short-time dynamics of ionic liquids has been investigated by low-frequency Raman spectroscopy (4 < omega < 100 cm(-1)) within the supercooled liquid range. Raman spectra are reported for ionic liquids with the same anion, bis(trifluoromethylsulfonyl)imide, and different cations: 1-butyl-3-methylimidazolium, 1-hexyl-3-methylimidazolium, 1-butyl-1-methylpiperidinium, trimethylbutylammonium, and tributylmethylammonium. It is shown that low-frequency Raman spectroscopy provides similar results as optical Kerr effect (OKE) spectroscopy, which has been used to study intermolecular vibrations in ionic liquids. The comparison of ionic liquids containing aromatic and non-aromatic cations identifies the characteristic feature in Raman spectra usually assigned to librational motion of the imidazolium ring. The strength of the fast relaxations (quasi-elastic scattering, QES) and the intermolecular vibrational contribution (boson peak) of ionic liquids with non-aromatic cations are significantly lower than imidazolium ionic liquids. A correlation length assigned to the boson peak vibrations was estimated from the frequency of the maximum of the boson peak and experimental data of sound velocity. The correlation length related to the boson peak (similar to 19 angstrom) does not change with the length of the alkyl chain in imidazolium cations, in contrast to the position of the first-sharp diffraction peak observed in neutron and X-ray scattering measurements of ionic liquids. The rate of change of the QES intensity in the supercooled liquid range is compared with data of excess entropy, free volume, and mean-squared displacement recently reported for ionic liquids. The temperature dependence of the QES intensity in ionic liquids illustrates relationships between short-time dynamics and long-time structural relaxation that have been proposed for glass-forming liquids. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3604533]

Beyond perfection : on relaxations and superclasses

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2006

Loss of connexin40 is associated with decreased endothelium-dependent relaxations and eNOS levels in the mouse aorta.

Upon agonist stimulation, endothelial cells trigger smooth muscle relaxation through the release of relaxing factors such as nitric oxide (NO). Endothelial cells of mouse aorta are interconnected by gap junctions made of connexin40 (Cx40) and connexin37 (Cx37), allowing the exchange of signaling molecules to coordinate their activity. Wild-type (Cx40(+/+)) and hypertensive Cx40-deficient mice (Cx40(-/-)), which also exhibit a marked decrease of Cx37 in the endothelium, were used to investigate the link between the expression of endothelial connexins (Cx40 and Cx37) and endothelial nitric oxide synthase (eNOS) expression and function in the mouse aorta. With the use of isometric tension measurements in aortic rings precontracted with U-46619, a stable thromboxane A(2) mimetic, we first demonstrate that ACh- and ATP-induced endothelium-dependent relaxations solely depend on NO release in both Cx40(+/+) and Cx40(-/-) mice, but are markedly weaker in Cx40(-/-) mice. Consistently, both basal and ACh- or ATP-induced NO production were decreased in the aorta of Cx40(-/-) mice. Altered relaxations and NO release from aorta of Cx40(-/-) mice were associated with lower expression levels of eNOS in the aortic endothelium of Cx40(-/-) mice. Using immunoprecipitation and in situ ligation assay, we further demonstrate that eNOS, Cx40, and Cx37 tightly interact with each other at intercellular junctions in the aortic endothelium of Cx40(+/+) mice, suggesting that the absence of Cx40 in association with altered Cx37 levels in endothelial cells from Cx40(-/-) mice participate to the decreased levels of eNOS. Altogether, our data suggest that the endothelial connexins may participate in the control of eNOS expression levels and function.

Endothelial nitric oxide synthase gene transfer restores endothelium-dependent relaxations and attenuates lesion formation in carotid arteries in apolipoprotein E-deficient mice.

Nitric oxide (NO) and monocyte chemoattractant protein-1 (MCP-1) exert partly opposing effects in vascular biology. NO plays pleiotropic vasoprotective roles including vasodilation and inhibition of platelet aggregation, smooth muscle cell proliferation, and endothelial monocyte adhesion, the last effect being mediated by MCP-1 downregulation. Early stages of arteriosclerosis are associated with reduced NO bioactivity and enhanced MCP-1 expression. We have evaluated adenovirus-mediated gene transfer of human endothelial NO synthase (eNOS) and of a N-terminal deletion (8ND) mutant of the MCP-1 gene that acts as a MCP-1 inhibitor in arteriosclerosis-prone, apolipoprotein E-deficient (ApoE(-/-)) mice. Endothelium-dependent relaxations were impaired in carotid arteries instilled with a noncoding adenoviral vector but were restored by eNOS gene transfer (p < 0.01). A perivascular collar was placed around the common carotid artery to accelerate lesion formation. eNOS gene transfer reduced lesion surface areas, intima/media ratios, and macrophage contents in the media at 5-week follow-up (p < 0.05). In contrast, 8ND-MCP-1 gene transfer did not prevent lesion formation. In conclusion, eNOS gene transfer restores endothelium-dependent vasodilation and inhibits lesion formation in ApoE(-/-) mouse carotids. Further studies are needed to assess whether vasoprotection is maintained at later disease stages and to evaluate the long-term efficacy of eNOS gene therapy for primary arteriosclerosis.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.

Multiplicative noise effects on relaxations from marginal states

Relaxational processes in bistable potentials close to marginal conditions are studied under the combined effect of additive and multiplicative fluctuations. Characteristic time scales associated with the first-passage-time-distribution are analytically obtained. Multiplicative noise introduces large effects on the characteristic decay times, which is particularly significant when relaxations are mediated by fluctuations, i.e., below marginality and for small noise intensity. The relevance of our approach with respect to realistic chemical bistable systems experimentally operated under external noise influences is mentioned.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Conductance and relaxations of gelatin films in the glassy and rubbery states

The dielectric constant, epsilon', and the dielectric loss, epsilon'', for gelatin films were measured in the glassy and rubbery states over a frequency range from 20 Hz to 10 MHz; epsilon' and epsilon'' were transformed into M* formalism (M* = 1/(epsilon' - i epsilon'') = M' + iM''; i, the imaginary unit). The peak of epsilon'' was masked probably due to dc conduction, but the peak of M'', e.g. the conductivity relaxation, for the gelatin used was observed. By fitting the M'' data to the Havriliak-Negami type equation, the relaxation time, tauHN, was evaluated. The value of the activation energy, Etau, evaluated from an Arrhenius plot of 1/tauHN, agreed well with that of Esigma evaluated from the DC conductivity sigma0 both in the glassy and rubbery states, indicating that the conductivity relaxation observed for the gelatin films was ascribed to ionic conduction. The value of the activation energy in the glassy state was larger than that in the rubbery state.

Calculating the Best Dual Bound for Problems with Multiple Lagrangian Relaxations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Atypical beta-adrenoceptor subtypes mediate relaxations of rabbit corpus cavernosum

This study was performed to characterize the beta-adrenoceptor population in rabbit isolated corpus cavernosum (RbCC) by using nonselective and selective beta-adrenoceptor agonists and antagonists in functional assays. Metaproterenol, ritodrine, fenoterol, and 8-hydroxy-5-[(1R)-1-hydroxy-2-[N-[(1R)-2-(rho-methoxy-phenyl)1-methylethyl] amino] ethyl] carbostyril (TA 2005) (3-100 nmol each) dose dependently relaxed the RbCC preparations. These relaxations were markedly reduced by N-omega-nitro-L-arginine methyl ester (L-NAME; 10 muM) and 1H-[1,2,4]-oxadiazolo-[4,3,-a]quinoxalin-1-one (ODQ) (10 muM), whereas the adenylyl cyclase inhibitor SQ 22,536 [9-(2-tetrahydrofuryl)adenine] (10 muM) had no effect. In contrast, neither L-NAME nor ODQ affected the isoproterenol-induced RbCC relaxations, but SQ 22,536 abolished this response. Sildenafil (1 muM) significantly potentiated the relaxations induced by beta(2)-agonists without affecting the isoproterenol-evoked relaxations. Rolipram (10 muM) enhanced the relaxations elicited by isoproterenol but had no effect on those induced by the selective beta(2) agonists. Propranolol and (+/-)-1-[2,3-(dihydro-7-methyl-1H-inden-4-yl)oxy]-3-[(1-methylethyl)amino]-2-butanolhydrochloride (ICI 118,551) determined a rightward shift in the concentration-response curves to isoproterenol in a noncompetitive manner with a reduction of maximum response at the highest antagonist concentration, with the slope values significantly different from unity. Propranolol and ICI 118,551 had no effect on the relaxations elicited by fenoterol, TA 2005, metaproterenol, and ritodrine. Atenolol and 1-[2-((3-carbamoyl-4-hydroxy)phenoxy) ethylamino]-3-[4-(1-methyl-4-trifluoromethyl-2-imidazolyl)-phenoxy]2-propanol methanesulfonate (CGP 20712A) (0.1-10 muM) failed to affect the relaxations induced by all tested beta-adrenoceptor agonists. Our study revealed the existence of two atypical beta-adrenoceptors in the rabbit erectile tissue. Isoproterenol relaxes the rabbit cavernosal tissue by activating atypical beta-adrenoceptors coupled to adenylyl cyclase pathway, whereas the selective beta2-adrenoceptor agonists relax the RbCC tissue through another atypical beta-adrenoceptor subtype coupled to nitric oxide release from the sinusoidal endothelium.

Influence of the molecular architecture on the secondary relaxations of Poly(styrene-co-methylmethacrylate) copolymers

The processes of adsorption of grafted copolymers onto negatively charged surfaces were studied using a dissipative quartz crystal microbalance (D-QCM) and ellipsometry. The control parameters in the study of the adsorption are the existence or absence on the molecular architecture of grafted polyethyleneglycol (PEG) chains with different lengths and the chemical nature of the main chain, poly(allylamine) (PAH) or poly(L-lysine) (PLL). It was found out that the adsorption kinetics of the polymers showed a complex behavior. The total adsorbed amount depends on the architecture of the polymer chains (length of the PEG chains), on the polymer concentration and on the chemical nature of the main chain. The comparison of the thicknesses of the adsorbed layers obtained from D-QCM and from ellipsometry allowed calculation of the water content of the layers that is intimately related to the grafting length. The analysis of D-QCM results also provides information about the shear modulus of the layers, whose values have been found to be typical of a rubber-like polymer system. It is shown that the adsorption of polymers with a charged backbone is not driven exclusively by the electrostatic interactions, but the entropic contributions as a result of the trapping of water in the layer structure are of fundamental importance.

Simulation of glassy state relaxations in polymers: A static analysis of methyl group and methoxy group rotation in poly(vinyl methyl ether)

We show that the simple quasi-static technique, also called the adiabatic mapping technique, can be used to determine the energetics of rotation of methyl and methoxy groups in amorphous poly(vinyl methyl ether) even though the latter process is too slow to be amenable to direct molecular dynamics simulation. For the methyl group rotation, we find that the mean and standard deviation of the simulated rotational barrier heights agree well with experimental data from quasi-elastic neutron scattering. In the case of the methoxy groups we find that just 4% of the groups contribute more than 90% of the observed dielectric relaxation strength. The groups which make the most contribution are those which, by virtue of their particular conformation and local environment, have two alternative positions of similar energy.

Water sorption-induced crystallization, structural relaxations and strength analysis of relaxation times in amorphous lactose/whey protein systems

Water sorption-induced crystallization, α-relaxations and relaxation times of freeze-dried lactose/whey protein isolate (WPI) systems were studied using dynamic dewpoint isotherms (DDI) method and dielectric analysis (DEA), respectively. The fractional water sorption behavior of lactose/WPI mixtures shown at aw ≤ 0.44 and the critical aw for water sorption-related crystallization (aw(cr)) of lactose were strongly affected by protein content based on DDI data. DEA results showed that the α-relaxation temperatures of amorphous lactose at various relaxation times were affected by the presence of water and WPI. The α-relaxation-derived strength parameter (S) of amorphous lactose decreased with aw up to 0.44 aw but the presence of WPI increased S. The linear relationship for aw(cr) and S for lactose/WPI mixtures was also established with R2 > 0.98. Therefore, DDI offers another structural investigation of water sorption-related crystallization as governed by aw(cr), and S may be used to describe real time effects of structural relaxations in noncrystalline multicomponent solids.